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Transcript of Friction
PHYSICS CHAP:5 LAWS OF MOTION Page 1
Static and limiting friction
1. The coefficient of friction and the angle of friction are
related as
(a) sin (b) cos
(c) tan (d) tan
2. A force of 98 N is required to just start moving a body of mass 100 kg over ice. The coefficient of static friction is
(a) 0.6 (b) 0.4
(c) 0.2 (d) 0.1
3. A block weighs W is held against a vertical wall by applying a horizontal force F. The minimum value of F needed to hold the block is
(a) Less than W (b) Equal to W
(c) Greater than W (d) Data is insufficient
4. The maximum static frictional force is
(a) Equal to twice the area of surface in contact
(b) Independent of the area of surface in contact
(c) Equal to the area of surface in contact
(d) None of the above
5. Maximum value of static friction is called
(a) Limiting friction (b) Rolling friction
(c) Normal reaction (d) Coefficient of friction
6. Pulling force making an angle to the horizontal is applied on a
block of weight W placed on a horizontal table. If the angle of
friction is , then the magnitude of force required to move the
body is equal to
(a) )tan(
sin
g
W (b)
)cos(
cos
W
(c) )cos(
sin
W (d)
)sin(
tan
W
7. In the figure shown, a block of weight 10 N resting on a
horizontal surface. The coefficient of static friction between the
block and the surface 4.0s . A force of 3.5 N will keep the
block in uniform motion, once it has been set in motion. A
horizontal force of 3 N is applied to the block, then the block will
(a) Move over the surface with constant velocity
(b) Move having accelerated motion over the surface
(c) Not move
(d) First it will move with a constant velocity for some time and
then will have accelerated motion
8. Two masses A and B of 10 kg and 5 kg respectively are
connected with a string passing over a frictionless pulley fixed
at the corner of a table as shown. The coefficient of static
friction of A with table is 0.2. The minimum mass of C that may
be placed on A to prevent it from moving is
(a) 15 kg
(b) 10 kg
(c) 5 kg
(d) 12 kg
9. The limiting friction is
(a) Always greater than the dynamic friction
(b) Always less than the dynamic friction
(c) Equal to the dynamic friction
(d) Sometimes greater and sometimes less than the dynamic
friction
10. Which is a suitable method to decrease friction
(a) Ball and bearings (b) Lubrication
(c) Polishing (d) All the above
11. A uniform rope of length l lies on a table. If the coefficient
of friction is , then the maximum length 1l of the part of
this rope which can overhang from the edge of the table
without sliding down is
(a)
l (b)
l
l
(c)
1
l (d)
1
l
12. Which of the following statements is not true
(a) The coefficient of friction between two surfaces
increases as the surface in contact are made rough
(b) The force of friction acts in a direction opposite to
the applied force
(c) Rolling friction is greater than sliding friction
(d) The coefficient of friction between wood and wood is
less than 1
13. A block of 1 kg is stopped against a wall by applying a
force F perpendicular to the wall. If 2.0 then
minimum value of F will be
(a) 980 N (b) 49 N
(c) 98 N (d) 490 N
14. A heavy uniform chain lies on a horizontal table-top. If
the coefficient of friction between the chain and table
surface is 0.25, then the maximum fraction of length of
the chain, that can hang over one edge of the table is
(a) 20% (b) 25%
(c) 35% (d) 15%
15. The blocks A and B are arranged as shown in the figure.
The pulley is frictionless. The mass of A is 10 kg. The
coefficient of friction of A with the horizontal surface is
0.20. The minimum mass of B to start the motion will be
(a) 2 kg
(b) 0.2 kg
(c) 5 kg
(d) 10 kg
T
A
C
B
A
B
PHYSICS CHAP:5 LAWS OF MOTION Page 2
16. Work done by a frictional force is
(a) Negative (b) Positive
(c) Zero (d) All of the above
17. A uniform chain of length L changes partly from a table
which is kept in equilibrium by friction. The maximum
length that can withstand without slipping is l, then
coefficient of friction between the table and the chain is
(a) L
l (b)
lL
l
(c) lL
l
(d)
lL
L
18. When two surfaces are coated with a lubricant, then they
(a) Stick to each other (b) Slide upon each other
(c) Roll upon each other (d) None of these
19. A 20 kg block is initially at rest on a rough horizontal
surface. A horizontal force of 75 N is required to set the
block in motion. After it is in motion, a horizontal force of
60 N is required to keep the block moving with constant
speed. The coefficient of static friction is
(a) 0.38 (b) 0.44
(c) 0.52 (d) 0.60
20. A block A with mass 100 kg is resting on another block B
of mass 200 kg. As shown in figure a horizontal rope tied
to a wall holds it. The coefficient of friction between A
and B is 0.2 while coefficient of friction between B and
the ground is 0.3. The minimum required force F to start
moving B will be
(a) 900 N
(b) 100 N
(c) 1100 N
(d) 1200 N
21. To avoid slipping while walking on ice, one should take
smaller steps because of the
(a) Friction of ice is large
(b) Larger normal reaction
(c) Friction of ice is small
(d) Smaller normal reaction
22. A box is lying on an inclined plane what is the coefficient
of static friction if the box starts sliding when an angle of
inclination is 60o
(a) 1.173 (b) 1.732
(c) 2.732 (d) 1.677
23. A block of mass 2 kg is kept on the floor. The coefficient
of static friction is 0.4. If a force F of 2.5 Newtons is
applied on the block as shown in the figure, the frictional
force between the block and the floor will be
(a) 2.5 N
(b) 5 N
(c) 7.84 N
(d) 10 N
24. Which one of the following is not used to reduce friction
(a) Oil (b) Ball bearings
(c) Sand (d) Graphite
25. If a ladder weighing 250N is placed against a smooth
vertical wall having coefficient of friction between it and
floor is 0.3, then what is the maximum force of friction
available at the point of contact between the ladder and
the floor
(a) 75 N (b) 50 N
(c) 35 N (d) 25 N
26. A body of mass 2 kg is kept by pressing to a vertical wall
by a force of 100 N. The coefficient of friction between
wall and body is 0.3. Then the frictional force is equal to
(a) 6 N (b) 20 N
(c) 600 N (d) 700 N
27. A horizontal force of 10 N is necessary to just hold a
block stationary against a wall. The coefficient of friction
between the block and the wall is 0.2. the weight of the
block is
(a) 2 N
(b) 20 N
(c) 50 N
(d) 100 N
28. The coefficient of static friction, ,s between block A of
mass 2 kg and the table as shown in the figure is 0.2.
What would be the maximum mass value of block B so
that the two blocks do not move? The string and the
pulley are assumed to be smooth and massless.
)/10( 2smg
(a) 2.0 kg
(b) 4.0 kg
(c) 0.2 kg
(d) 0.4 kg
29. If mass of kgA 10 , coefficient of static friction = 0.2,
coefficient of kinetic friction = 0.2. Then mass of B to
start motion is
(a) 2 kg
(b) 2.2 kg
(c) 4.8 kg
(d) 200 gm
30. A uniform metal chain is placed on a rough table such
that one end of chain hangs down over the edge of the
table. When one-third of its length hangs over the edge,
the chain starts sliding. Then, the coefficient of static
friction is
(a) 4
3 (b)
4
1
(c) 3
2 (d)
2
1
F
10 N
A
B
2 kg
A
B
10 kg
B
A
F
PHYSICS CHAP:5 LAWS OF MOTION Page 3
31. A lift is moving downwards with an acceleration equal to
acceleration due to gravity. A body of mass m kept on
the floor of the lift is pulled horizontally. If the coefficient
of friction is , then the frictional resistance offered by
the body is
(a) mg (b) mg
(c) mg2 (d) Zero
32. If a ladder weighing 250 N is placed against a smooth
vertical wall having coefficient of friction between it and
floor is 0.3, then what is the maximum force of friction
available at the point of contact between the ladder and
the floor
(a) 75 N (b) 50 N
(c) 35 N (d) 25 N
Kinetic Friction
1. Which one of the following statements is correct
(a) Rolling friction is greater than sliding friction
(b) Rolling friction is less than sliding friction
(c) Rolling friction is equal to sliding friction
(d) Rolling friction and sliding friction are same
2. The maximum speed that can be achieved without
skidding by a car on a circular unbanked road of radius R
and coefficient of static friction , is
(a) Rg (b) Rg
(c) Rg (d) Rg
3. A car is moving along a straight horizontal road with a
speed 0v . If the coefficient of friction between the tyres
and the road is , the shortest distance in which the car
can be stopped is
(a) g
v
2
20 (b)
g
v
0
(c)
2
0
g
v
(d)
0v
4. A block of mass 5 kg is on a rough horizontal surface and
is at rest. Now a force of 24 N is imparted to it with
negligible impulse. If the coefficient of kinetic friction is
0.4 and 2/8.9 smg , then the acceleration of the block is
(a) 2/26.0 sm (b) 2/39.0 sm
(c) 2/69.0 sm (d) 2/88.0 sm
5. A body of mass 2 kg is being dragged with uniform
velocity of 2 m/s on a rough horizontal plane. The
coefficient of friction between the body and the surface
is 0.20. The amount of heat generated in 5 sec is
caljouleJ /2.4( and )/8.9 2smg
(a) 9.33 cal (b) 10.21 cal
(c) 12.67 cal (d) 13.34 cal
6. Two carts of masses 200 kg and 300 kg on horizontal
rails are pushed apart. Suppose the coefficient of friction
between the carts and the rails are same. If the 200 kg
cart travels a distance of 36 m and stops, then the
distance travelled by the cart weighing 300 kg is
(a) 32 m (b) 24 m
(c) 16 m (d) 12 m
7. A body B lies on a smooth horizontal table and another
body A is placed on B. The coefficient of friction between
A and B is . What acceleration given to B will cause
slipping to occur between A and B
(a) g (b) /g
(c) g/ (d) g
8. A 60 kg body is pushed with just enough force to start it
moving across a floor and the same force continues to
act afterwards. The coefficient of static friction and
sliding friction are 0.5 and 0.4 respectively. The
acceleration of the body is
(a) 2/6 sm (b) 2/9.4 sm
(c) 2/92.3 sm (d) 2/1 sm
9. A car turns a corner on a slippery road at a constant
speed of sm /10 . If the coefficient of friction is 0.5, the
minimum radius of the arc in meter in which the car turns
is
(a) 20 (b) 10
(c) 5 (d) 4
10. A motorcyclist of mass m is to negotiate a curve of radius
r with a speed v. The minimum value of the coefficient of
friction so that this negotiation may take place safely, is
(a) rgv2 (b) gr
v 2
(c) 2v
gr (d)
rv
g2
11. On a rough horizontal surface, a body of mass 2 kg is
given a velocity of 10 m/s. If the coefficient of friction is
0.2 and 2/10 smg , the body will stop after covering a
distance of
(a) 10 m (b) 25 m
(c) 50 m (d) 250 m
12. A block of mass 50 kg can slide on a rough horizontal
surface. The coefficient of friction between the block and
the surface is 0.6. The least force of pull acting at an
angle of 30° to the upward drawn vertical which causes
the block to just slide is
(a) 29.43 N (b) 219.6 N
(c) 21.96 N (d) 294.3 N
13. A body of 10 kg is acted by a force of 129.4 N if 2sec/8.9 mg . The acceleration of the block is 2/10 sm .
What is the coefficient of kinetic friction
(a) 0.03 (b) 0.01
(c) 0.30 (d) 0.25
A B
PHYSICS CHAP:5 LAWS OF MOTION Page 4
14. Assuming the coefficient of friction between the road
and tyres of a car to be 0.5, the maximum speed with
which the car can move round a curve of 40.0 m radius
without slipping, if the road is unbanked, should be
(a) 25 m/s (b) 19 m/s
(c) 14 m/s (d) 11 m/s
15. Consider a car moving along a straight horizontal road
with a speed of 72 km/h. If the coefficient of kinetic
friction between the tyres and the road is 0.5, the
shortest distance in which the car can be stopped is
]10[ 2 msg
(a) 30 m (b) 40 m
(c) 72 m (d) 20 m
16. A 500 kg horse pulls a cart of mass 1500 kg along a level
road with an acceleration of 21 ms . If the coefficient of
sliding friction is 0.2, then the force exerted by the horse
in forward direction is
(a) 3000 N (b) 4000 N
(c) 5000 N (d) 6000 N
17. The maximum speed of a car on a road turn of radius
30m; if the coefficient of friction between the tyres and
the road is 0.4; will be
(a) 9.84 m/s (b) 10.84 m/s
(c) 7.84 m/s (d) 5.84 m/s
18. A block of mass 50 kg slides over a horizontal distance of
1 m. If the coefficient of friction between their surfaces
is 0.2, then work done against friction is
(a) 98 J (b) 72J
(c) 56 J (d) 34 J
19. On the horizontal surface of a truck ( = 0.6), a block of
mass 1 kg is placed. If the truck is accelerating at the
rate of 5m/sec2 then frictional force on the block will be
(a) 5 N (b) 6 N
(c) 5.88 N (d) 8 N
20. A vehicle of mass m is moving on a rough horizontal road
with momentum P. If the coefficient of friction between
the tyres and the road be , then the stopping distance is
(a) gm
P
2 (b)
gm
P
2
2
(c) gm
P22
(d) gm
P2
2
2
21. A body of weight 64 N is pushed with just enough force to
start it moving across a horizontal floor and the same
force continues to act afterwards. If the coefficients of
static and dynamic friction are 0.6 and 0.4 respectively,
the acceleration of the body will be (Acceleration due to
gravity = g)
(a) 4.6
g (b) 0.64 g
(c) 32
g (d) 0.2 g
22. When a body is moving on a surface, the force of friction
is called
(a) Static friction (b) Dynamic friction
(c) Limiting friction (d) Rolling friction
23. A block of mass 10 kg is placed on a rough horizontal
surface having coefficient of friction = 0.5. If a
horizontal force of 100 N is acting on it, then acceleration
of the block will be
(a) 0.5 m/s2 (b) 5 m/s2
(c) 10 m/s2 (d) 15 m/s2
24. It is easier to roll a barrel than pull it along the road. This
statement is
(a) False (b) True
(c) Uncertain (d) Not possible
25. A marble block of mass 2 kg lying on ice when given a
velocity of 6 m/s is stopped by friction in 10s. Then the
coefficient of friction is
(a) 0.01 (b) 0.02
(c) 0.03 (d) 0.06
26. A horizontal force of 129.4 N is applied on a 10 kg block
which rests on a horizontal surface. If the coefficient of
friction is 0.3, the acceleration should be
(a) 2/8.9 sm (b) 2/10 sm
(c) 2/6.12 sm (d) 2/6.19 sm
27. A 60 kg weight is dragged on a horizontal surface by a
rope upto 2 metres. If coefficient of friction is 5.0 , the
angle of rope with the surface is 60° and 2sec/8.9 mg ,
then work done is
(a) 294 joules (b) 315 joules
(c) 588 joules (d) 197 joules
28. A car having a mass of 1000 kg is moving at a speed of
30 metres/sec. Brakes are applied to bring the car to
rest. If the frictional force between the tyres and the road
surface is 5000 newtons, the car will come to rest in
(a) 5 seconds (b) 10 seconds
(c) 12 seconds (d) 6 seconds
29. If ks , and r are coefficients of static friction, sliding
friction and rolling friction, then
(a) rks (b) srk
(c) skr (d) skr
30. A body of mass 5kg rests on a rough horizontal surface
of coefficient of friction 0.2. The body is pulled through a
distance of 10m by a horizontal force of 25 N. The kinetic
energy acquired by it is (g = 10 ms2)
(a) 330 J (b) 150 J
(c) 100 J (d) 50 J
31. A motorcycle is travelling on a curved track of radius
500m. If the coefficient of friction between road and tyres
is 0.5, the speed avoiding skidding will be
(a) 50 m/s (b) 75 m/s
PHYSICS CHAP:5 LAWS OF MOTION Page 5
(c) 25 m/s (d) 35 m/s
32. A fireman of mass 60 kg slides down a pole. He is
pressing the pole with a force of 600 N. The coefficient
of friction between the hands and the pole is 0.5, with
what acceleration will the fireman slide down (g = 10
m/s2)
(a) 1 m/s2 (b) 2.5 m/s2
(c) 10 m/s2 (d) 5 m/s2
33. A block of mass kgM 5 is resting on a rough horizontal
surface for which the coefficient of friction is 0.2. When a
force NF 40 is applied, the acceleration of the block
will be )/10( 2smg
(a) 2sec/73.5 m
(b) 2sec/0.8 m
(c) 2sec/17.3 m
(d) 2sec/0.10 m
34. A body is moving along a rough horizontal surface with
an initial velocity ./6 sm If the body comes to rest after
travelling 9 m, then the coefficient of sliding friction will
be
(a) 0.4 (b) 0.2
(c) 0.6 (d) 0.8
35. Consider a car moving on a straight road with a speed of
100 m/s. The distance at which car can be stopped is
]5.0[ k
(a) 100 m (b) 400 m
(c) 800 m (d) 1000 m
36. A cylinder of 10 kg is sliding in a plane with an initial
velocity of 10 m/s. If the coefficient of friction between
the surface and cylinder is 0.5 then before stopping, it
will cover. )/10( 2smg
(a) 2.5 m (b) 5 m
(c) 7.5 m (d) 10 m
Motion on Inclined Surface
1. When a body is lying on a rough inclined plane and does
not move, the force of friction
(a) is equal to R (b) is less than R
(c) is greater than R (d) is equal to R
2. When a body is placed on a rough plane inclined at an
angle to the horizontal, its acceleration is
(a) )cos(sin g (b) )cos(sin g
(c) )cos1sin( g (d) )cos(sin g
3. A block is at rest on an inclined plane making an angle
with the horizontal. As the angle of the incline is
increased, the block starts slipping when the angle of
inclination becomes . The coefficient of static friction
between the block and the surface of the inclined plane
is or
A body starts sliding down at an angle to horizontal.
Then coefficient of friction is equal to
(a) sin (b) cos
(c) tan (d) Independent of
4. A given object takes n times as much time to slide down
a 45° rough incline as it takes to slide down a perfectly
smooth 45° incline. The coefficient of kinetic friction
between the object and the incline is given by
(a)
2
11
n (b)
21
1
n
(c)
2
11
n (d)
21
1
n
5. The force required just to move a body up an inclined
plane is double the force required just to prevent the
body sliding down. If the coefficient of friction is 0.25, the
angle of inclination of the plane is
(a) 36.8° (b) 45°
(c) 30° (d) 42.6°
6. Starting from rest, a body slides down a 45° inclined
plane in twice the time it takes to slide down the same
distance in the absence of friction. The coefficient of
friction between the body and the inclined plane is
(a) 0.33 (b) 0.25
(c) 0.75 (d) 0.80
7. The coefficient of friction between a body and the
surface of an inclined plane at 45° is 0.5. If 2/8.9 smg ,
the acceleration of the body downwards in 2/ sm is
(a) 2
9.4 (b) 29.4
(c) 26.19 (d) 4.9
8. A box is placed on an inclined plane and has to be
pushed down. The angle of inclination is
(a) Equal to angle of friction
(b) More than angle of friction
(c) Equal to angle of repose
(d) Less than angle of repose
9. A force of 750 N is applied to a block of mass 102 kg to
prevent it from sliding on a plane with an inclination
angle 30° with the horizontal. If the coefficients of static
friction and kinetic friction between the block and the
plane are 0.4 and 0.3 respectively, then the frictional
force acting on the block is
(a) 750 N (b) 500 N
(c) 345 N (d) 250 N
10. A block is lying on an inclined plane which makes 60°
with the horizontal. If coefficient of friction between
block and plane is 0.25 and 2/10 smg , then
acceleration of the block when it moves along the plane
will be
M
F
30°
PHYSICS CHAP:5 LAWS OF MOTION Page 6
(a) 2/50.2 sm (b) 2/00.5 sm
(c) 2/4.7 sm (d) 2/66.8 sm
11. A body of mass 100 g is sliding from an inclined plane of
inclination 30°. What is the frictional force experienced if
7.1
(a) N3
127.1 (b) N
2
137.1
(c) N37.1 (d) N3
127.1
12. A body takes just twice the time as long to slide down a
plane inclined at 30o to the horizontal as if the plane were
frictionless. The coefficient of friction between the body
and the plane is
(a) 4
3 (b) 3
(c) 3
4 (d)
4
3
13. A brick of mass 2 kg begins to slide down on a plane
inclined at an angle of 45o with the horizontal. The force
of friction will be
(a) 19.6 sin 45o (b) 19.6 cos 45o
(c) 9.8 sin 45o (d) 9.8 cos 45o
14. The upper half of an inclined plane of inclination is
perfectly smooth while the lower half is rough. A body
starting from the rest at top comes back to rest at the
bottom if the coefficient of friction for the lower half is
given by
(a) = sin (b) = cot
(c) = 2 cos (d) = 2 tan
15. A body is sliding down an inclined plane having
coefficient of friction 0.5. If the normal reaction is twice
that of the resultant downward force along the incline,
the angle between the inclined plane and the horizontal
is
(a) 15o (b) 30 o
(c) 45 o (d) 60 o
16. A body of mass 10 kg is lying on a rough plane inclined at
an angle of 30o to the horizontal and the coefficient of
friction is 0.5. the minimum force required to pull the
body up the plane is
(a) 914 N (b) 91.4 N
(c) 9.14 N (d) 0.914 N
17. A block of mass 1 kg slides down on a rough inclined
plane of inclination 60o starting from its top. If the
coefficient of kinetic friction is 0.5 and length of the plane
is 1 m, then work done against friction is (Take g = 9.8
m/s2)
(a) 9.82 J (b) 4.94 J
(c) 2.45J (d) 1.96 J
18. A block of mass 10 kg is placed on an inclined plane.
When the angle of inclination is 30o, the block just begins
to slide down the plane. The force of static friction is
(a) 10 kg wt (b) 89 kg w
(c) 49 kg wt (d) 5 kg wt
19. A body of 5 kg weight kept on a rough inclined plane of
angle 30o starts sliding with a constant velocity. Then the
coefficient of friction is (assume g = 10 m/s2)
(a) 3/1 (b) 3/2
(c) 3 (d) 32
20. 300 Joule of work is done in sliding up a 2 kg block on an
inclined plane to a height of 10 metres. Taking value of
acceleration due to gravity ‘g’ to be 10 m/s2, work done
against friction is
(a) 100 J (b) 200 J
(c) 300 J (d) Zero
21. A 2 kg mass starts from rest on an inclined smooth
surface with inclination 30o and length 2 m. How much
will it travel before coming to rest on a frictional surface
with frictional coefficient of 0.25
(a) 4 m (b) 6 m
(c) 8 m (d) 2 m
22. A block rests on a rough inclined plane making an angle
of o30 with the horizontal. The coefficient of static
friction between the block and the plane is 0.8. If the
frictional force on the block is 10 N, the mass of the
block (in kg) is (take )/10 2smg
(a) 2.0 (b) 4.0
(c) 1.6 (d) 2.5
23. A body takes time t to reach the bottom of an inclined
plane of angle with the horizontal. If the plane is made
rough, time taken now is 2t. The coefficient of friction of
the rough surface is
(a) tan4
3 (b) tan
3
2
(c) tan4
1 (d) tan
2
1
24. A block is kept on an inclined plane of inclination of
length l. The velocity of particle at the bottom of inclined
is (the coefficient of friction is )
(a) )sincos(2 gl (b) )cos(sin2 gl
(c) )cos(sin2 gl (d) )sin(cos2 gl
CRITICAL QUESTIONS
1. A block of mass m lying on a rough horizontal plane is
acted upon by a horizontal force P and another force Q
inclined at an angle to the vertical. The block will
remain in equilibrium, if the coefficient of friction
between it and the surface is
(a) )cos(
)sin(
Qmg
QP
(b) )sin(
)cos(
Qmg
QP
(c) )sin(
)cos(
Qmg
QP
(d) )cos(
)sin(
Qmg
QP
M
Q
P
PHYSICS CHAP:5 LAWS OF MOTION Page 7
2. Which of the following is correct, when a person walks
on a rough surface
(a) The frictional force exerted by the surface keeps him
moving
(b) The force which the man exerts on the floor keeps
him moving
(c) The reaction of the force which the man exerts on
floor keeps him moving
(d) None of the above
3. A block of mass 0.1 kg is held against a wall by applying
a horizontal force of 5 N on the block. If the coefficient of
friction between the block and the wall is 0.5, the
magnitude of the frictional force acting on the block is
(a) 2.5 N (b) 0.98 N
(c) 4.9 N (d) 0.49 N
4. A body of mass M is kept on a rough horizontal surface
(friction coefficient ). A person is trying to pull the
body by applying a horizontal force but the body is not
moving. The force by the surface on the body is F, where
(a) MgF (b) MgfF
(c) 21 MgFMg (d) 21 MgFMg
5. What is the maximum value of the force F such that the
block shown in the arrangement, does not move
(a) 20 N (b) 10 N
(c) 12 N (d) 15 N
6. A block P of mass m is placed on a frictionless horizontal
surface. Another block Q of same mass is kept on P and
connected to the wall with the help of a spring of spring
constant k as shown in the figure. s is the coefficient of
friction between P and Q. The blocks move together
performing SHM of amplitude A. The maximum value of
the friction force between P and Q is
(a) kA
(b) 2
kA
(c)Zero
(d) mgs
7. A body of mass m rests on horizontal surface. The
coefficient of friction between the body and the surface
is . If the mass is pulled by a force P as shown in the
figure, the limiting friction between body and surface will
be
(a) mg
(b)
2
Pmg
(c)
2
Pmg
(d)
2
3 Pmg
8. A 40 kg slab rests on a frictionless floor as shown in the
figure. A 10 kg block rests on the top of the slab. The
static coefficient of friction between the block and slab is
0.60 while the kinetic friction is 0.40. The 10 kg block is
acted upon by a horizontal force 100 N. If 2/8.9 smg ,
the resulting acceleration of the slab will be
(a) 2/98.0 sm
(b) 2/47.1 sm
(c) 2/52.1 sm
(d) 2/1.6 sm
9. A block of mass 2 kg rests on a rough inclined plane
making an angle of 30° with the horizontal. The
coefficient of static friction between the block and the
plane is 0.7. The frictional force on the block is
(a) 9.8 N
(b) N38.97.0
(c) N38.9
(d) N8.98.0
10. When a bicycle is in motion, the force of friction exerted
by the ground on the two wheels is such that it acts
(a) In the backward direction on the front wheel and in
the forward direction on the rear wheel
(b) In the forward direction on the front wheel and in the
backward direction on the rear wheel
(c) In the backward direction on both front and the rear
wheels
(d) In the forward direction on both front and the rear
wheels
11. An insect crawls up a hemispherical surface very slowly
(see the figure). The coefficient of friction between the
insect and the surface is 1/3. If the line joining the centre
of the hemispherical surface to the insect makes an
angle with the vertical, the maximum possible value of
is given by
(a) 3cot
(b) 3tan
(c) 3sec
(d) 3cosec
m
P 30°
100 N 10 kg
40 kg
A
B
F
60°
32
1
m=3kg
Smooth
surface
P
Q
PHYSICS CHAP:5 LAWS OF MOTION Page 8
Static and Limiting Friction
1 c 2 D 3 c 4 b 5 a
6 c 7 C 8 a 9 a 10 d
11 c 12 C 13 b 14 a 15 A
16 d 17 C 18 b 19 a 20 C
21 c 22 B 23 a 24 c 25 A
26 b 27 A 28 d 29 a 30 D
31 d 32 A
Kinetic Friction
1 b 2 d 3 A 4 d 5 A
6 c 7 a 8 D 9 a 10 B
11 b 12 d 13 C 14 c 15 B
16 d 17 b 18 A 19 a 20 D
21 d 22 b 23 B 24 b 25 D
26 b 27 b 28 D 29 c 30 B
31 a 32 d 33 A 34 b 35 D
36 d
Motion on Inclined Surface
1 b 2 b 3 c 4 a 5 A
6 c 7 a 8 d 9 d 10 C
11 b 12 a 13 a 14 d 15 C
16 b 17 c 18 d 19 a 20 A
21 a 22 a 23 a 24 b
Critical Thinking Questions
1 a 2 c 3 b 4 c 5 A
6 b 7 c 8 a 9 a 10 ac
11 a
PHYSICS CHAP:5 LAWS OF MOTION Page 9
Static and Limiting Friction
1. (c)
2. (d) 1.010
1
8.9100
98
mg
F
R
F
3. (c) Here applied horizontal force F acts as normal reaction.
For holding the block
Force of friction = Weight of block
Wf WR WF
WF
As 1 WF
4. (b)
5. (a)
6. (c)
7. (c) NmgRF sl 4104.04.0 i.e. minimum 4N force is
required to start the motion of a body. But applied force is only 3N. So the
block will not move.
8. (a) For limiting condition CA
B
mm
m
Cm
10
52.0
52.02 Cm kgmC 15
9. (a)
10. (d) Ball and bearing produce rolling motion for which force of friction is low.
Lubrication and polishing reduce roughness of surface.
11. (c) For given condition we can apply direct formula
ll
11
12. (c) Sliding friction is greater than rolling friction.
13. (b) NW
F 492.0
8.91
14. (a) %205125.0
25.0
1
'
llll
of l.
15. (a) kgmm
m
mB
B
A
B 210
2.0
16. (d) Work done by friction can be positive, negative and zero depending upon the
situation.
17. (c) table theonlying chainof Lenght
table thefromhanging chainof Lenght
lL
l
18. (b) Surfaces always slide over each other.
19. (a) Coefficient of friction 8.920
7575
mgR
Fls 38.0
20. (c)
BGAB ffF
gmmgm BABGaAB )(
101002.0
10)300(3.0
N1100900200
21. (c)
22. (b) tan (Angle of repose) 732.160tan
23. (a) Applied force N5.2
Limiting friction Nmg 84.78.924.0
For the given condition applied force is very smaller than limiting friction.
Static friction on a body = Applied force = 2.5 N
24. (c) Sand is used to increase the friction.
25. (a) NRF 752503.0
26. (b) For the given condition, Static friction
= Applied force = Weight of body N20102
27. (a)
WF NFW 2102.0
28. (d) A
Bs
m
m
22.0 Bm kgmB 4.0
29. (a) kgmm
m
mB
B
A
Bs 2
102.0
30. (d) table theonlying chain of the Length
table thefromhanging chain of the Lenghts
2
1
3/2
3/
3/
3/
l
l
ll
l
31. (d)
32. (a)
Kinetic Friction
1. (b)
2. (d) In the given condition the required centripetal force is provided by frictional force between the road and tyre.
mgR
mv
2
Rgv
3. (a) Retarding force mgRmaF ga
Now from equation of motion asuv 222
asu 20 2 g
u
a
us
22
22
g
v
2
20
4. (d) Net force = Applied force – Friction force
mgma 24 8.954.024 6.1924
f
W
R F
B
A
F fBG
fAB
Ground
PHYSICS CHAP:5 LAWS OF MOTION Page 10
2/88.05
4.4sma
5. (a) Work done = Force × Displacement )( tvmg
jouleW 528.92)2.0(
Heat generated QJ
W
2.4
528.922.0 33.9 cal
6. (c) For given condition2
1
ms
22
2
1
1
2
300
200
m
m
s
s
mss 169
436
9
412
7. (a) There is no friction between the body B and surface of the table. If the body B
is pulled with force F then
ammF BA )(
Due to this force upper body A will feel the pseudo force in a backward
direction.
amf A
But due to friction between A and B, body will not move. The body A will start
moving when pseudo force is more than friction force.
i.e. for slipping, gmam AA ga
8. (d) Limiting friction NmgR ss 30010605.0
Kinetic friction NmgR kk 24010604.0
Force applied on the body = 300 N and if the body is moving then, Net
accelerating force
=Applied force – Kinetic friction
60240300 ma 2/160
60sma
9. (a) 20105.0
1002
g
vrrgv
10. (b)
11. (b) mg
uS 25
102.02
)10(
2
22
12. (d)
For limiting condition Rf
)30cos(30sin FmgF , By solving NF 3.294
13. (c) Net force on the body = Applied force – Friction
mgFma k 3.08.910
10104.129
mg
maFk
14. (c) smgrv /14196408.95.0
15. (b) mg
us 40
105.02
)20(
2
22
16. (d) Net force in forward direction = Accelerating force + Friction
)102.01)(5001500()( gammgma
N600032000
17. (b) smrgv /84.108.9304.0
18. (a) JmgSW 9818.9502.0
19. (a) NmgFl 88.58.916.0
Pseudo force on the block = Nma 551
Pseudo is less then limiting friction hence static force of friction = 5 N.
20. (d) gm
P
gm
um
g
uS
2
2
2
222
222
21. (d) Weight of the body = 64N
so mass of the body kgm 4.6 , 6.0s , 4.0k
Net acceleration bodyof the Mass
frictionKinetic - force Applied
gggm
mgmgks
ks 2.0)4.06.0()(
22. (b)
23. (b) mass
frictionKinetic –force Applieda
2/510
10105.0100sm
24. (b)
25. (d) 0 gtuatuv 06.01010
6
gt
u
26. (b) From the relation mamgF
2/1010
8.9103.04.129sm
m
mgFa
27. (b) Let body is dragged with force P, making an angle 60° with the horizontal.
kF Kinetic friction in the motion = Rk
From the figure 60cosPFk and 60sinPmgR
)60sin(60cos PmgP k
2
310605.0
2
PP NP 1.315
NPFk2
1.31560cos
Work done JoulesFk 31522
1.315
28. (d) a
utatuv [As 0v ]
F
mut
sec6
5000
100030
29. (c)
B
A f
R F
F
F sin 30°
F cos 30°
f
mg
R
P
P cos 60°
P sin 60°
Fk
mg
60°
R
PHYSICS CHAP:5 LAWS OF MOTION Page 11
30. (b) Kinetic energy acquired by body
= (Total work done on the body) – (work against friction)
101052.01025 mgSSF
Joule150100250
31. (a) smrgv /50105005.0
32. (d) Net downward acceleration Mass
force Friction-Weight
m
Rmg )(
60
6005.01060
2/560
300sm
33. (a)
Kinetic friction = Rk )30sin(2.0 Fmg
2
1401052.0 N6)2050(2.0
Acceleration of the block Mass
frictionKinetic 30cos
F
2/73.55
62
340
sm
34. (b) We know g
us
2
2
2.09102
)6(
2
22
gs
u
35. (d) mg
us 1000
105.02
)100(
2
22
36. (d) Kinetic energy of the cylinder will go against friction
2
2
1mv = mgs m
g
us 10
10)5.0(2
)10(
2
22
Motion on Inclined Surface
1. (b) When the body is at rest then static friction works on it, which is less than
limiting friction )( R .
2. (b)
3. (c) Coefficient of friction = Tangent of angle of repose
tan
4. (a)
2
11tan
n
2
11
n [As 45 ]
5. (a) Retardation in upward motion )cos(sin g
Force required just to move up )cos(sin mgFup
Similarly for down ward motion a )cos(sin g
Force required just to prevent the body sliding down
)cos(sin mgFdn
According to problem dnup FF 2
)cos(sin2)cos(sin mgmg
cos2sin2cossin
sincos3 3tan
)75.0(tan)25.03(tan)3(tan 111 8.36
6. (c)
2
11tan
n
45 and 2n (Given)
75.04
3
4
11
2
1145tan
2
7. (a) )45cos5.05(sin8.9)cos(sin ooga
2sec/2
9.4m
8. (d) Because if the angle of inclination is equal to or more than angle of repose then
box will automatically slides down the plane.
9. (d)
s
Net force along the plane
= sinmgP = 500750 = N250
Limiting friction = cosmgRF ssl
= 0.4 × 102 × 9.8 × cos 30 = 346 N
As net external force is less than limiting friction therefore friction on the body
will be 250 N.
10. (c) )cos(sin ga )60cos25.060(sin10
2/4.7 sma
11. (b) cosmgRF kkk
30cos101.07.1kF N2
37.1
12. (a) 4
3
2
1130tan
11tan
22
n
13. (a) For angle of repose,
Friction =Component of weight along the plane
= sinmg o45sin8.92 o45sin6.19
14. (d) For upper half
sin2/)sin(22/222 gllgaluv
For lower half
2
)cos(sin20 2 lgu
W
R
F
600N
F
F cos 30°
F sin 30°
Fk
mg
30°
R
l/2
l/2
R
mg cos
F
P
mg
PHYSICS CHAP:5 LAWS OF MOTION Page 12
)cos(sinsin glgl
tan2sin2cos
15. (c) Resultant downward force along the incline
)cos(sin mg
Normal reaction cosmg
Given : )cos(sin2cos mgmg
By solving o45 .
16. (b) )cos(sin mgF
N4.91)30cos5.030(sin8.910 .
17. (c) JSmgW 45.212
18.915.0cos
18. (d) wtkgNmgF -55030sin .
19. (a) 3
130tan .
20. (a) Work done against gravity mgh J20010102
Work done against friction = (Total work done – work done against gravity)
J100200300
21. (a)
30sin20222 gasuv 2 20v
Let it travel distance ‘S’ before coming to rest
mg
vS 4
1025.02
20
2
2
22. (a) Angle of repose 6.38)8.0(tan)(tan 11
Angle of inclined plane is given 30 .
It means block is at rest therefore,
Static friction = component of weight in downward direction
Nmg 10sin kgm 230sin9
10
23. (a)
2
11tan
n tan
4
3
2
11tan
2
24. (b) Acceleration (a) )cos(sin g and s = l
asv 2 )cos(sin2 gl
Critical Thinking Questions
1. (a) By drawing the free body diagram of the block for critical condition
RF sinQP
)cos( Qmg
cos
sin
Qmg
QP
2. (c)
3. (b) Limiting friction
NRF sl 5.2)5(5.0
Since downward force is less than limiting friction therefore block is at rest so
the static force of friction will work on it.
sF = downward force = Weight
98.08.91.0 N
4. (c) Maximum force by surface when friction works
1)( 22222 RRRRfF
Minimum force R when there is no friction
Hence ranging from R to 12 R
We get, 12 MgFMg
5. (a)
Rf
)60sin(60cos FWF
Substituting 32
1 & 310W we get NF 20
6. (b) When two blocks performs simple harmonic motion together then at the extreme
position ( at amplitude =A)
Restoring force maKAF 2 m
KAa
2
There will be no relative motion between P and Q if pseudo force on block P is
less than or just equal to limiting friction between P and Q.
i.e.
m
KAm
2Limiting friction
Maximum friction 2
KA
7. (c) Normal reaction oPmgR 30sin2
Pmg
S
2m
30° Rough
R
mg + Q cos
F P+Q sin
R 5N
R
mg
310W
F
F cos 60
F sin 60
R
60°
f
F
P cos 30°
R + P sin 30°
mg
P
30°
PHYSICS CHAP:5 LAWS OF MOTION Page 13
Limiting friction between body and surface is given by,
2
PmgRF .
8. (a) Limiting friction between block and slab gm As
N8.588.9106.0
But applied force on block A is 100 N. So the block will slip over a slab.
Now kinetic friction works between block and slab gmF Akk
N2.398.9104.0
This kinetic friction helps to move the slab
Acceleration of slab 2/98.040
2.392.39sm
mB
9. (a) Limiting friction cosmgFl
NFl 1230cos1027.0 (approximately)
But when the block is lying on the inclined plane then component of weight
down the plane sinmg
N8.930sin8.92
It means the body is stationary, so static friction will work on it
Static friction = Applied force = 9.8 N
10. (a,c) In cycling, the rear wheel moves by the force communicated to it by pedalling
while front wheel moves by it self. So, while pedalling a bicycle, the force
exerted by rear wheel on ground makes force of friction act on it in the forward
direction (like walking). Front wheel moving by itself experience force of
friction in backward direction (like rolling of a ball). [However, if pedalling is
stopped both wheels move by themselves and so experience force of friction in
backward direction].
11. (a)